Harmonic oscillator transition kernel
= Harmonic oscillator transition kernel
{title2=$K_\omega(q_f,q_i;T)$}
For <action> $\frac m2\int(\dot q^2-\omega^2q^2)dt$, the kernel is $\sqrt{m\omega/(2\pi i\sin\omega T)}\exp\{im\omega[(q_f^2+q_i^2)\cos\omega T-2q_fq_i]/(2\sin\omega T)\}$. The <Dirichlet oscillator determinant ratio> supplies its prefactor, while the classical boundary <action> supplies its exponent. The <Feynman i-epsilon prescription> specifies its continuation through caustics.